The population of rats in my farm moves constantly back and forth between the house and the field. Every week 40% of the rats in the field move to my house while 30% of those in my house move to the field. Suppose that, initially, the distribution of this population is: 70% in the field and 30% in my house.

(a) Find the migration matrix and set up a difference equation for this situation. (b) What is the ratsí distribution after two week in my farm?

a) I get this migration matrix:

0.70 0.40
0.30 0.60

Is this correct? If so, how do I set up a difference equation?

b)

0.70 0.40
0.30 0.60

multiply this matrix by:

0.70
0.30

this will give the rats distribution after 1 week, and multiply by that again to get the distribution after two weeks. Is this correct?

Please can someone give me some guidance on this problem.

Dec 4th 2012, 05:32 AM

BobP

Re: matrix question

Just write what you are doing in matrix form

Dec 4th 2012, 07:17 AM

dumbledore

Re: matrix question

Yes I did write it in matrix form, which is why I said "I get this migration matrix" and then wrote it in matrix form.

Can someone help me with this problem please?

Dec 4th 2012, 08:10 AM

HallsofIvy

Re: matrix question

The "difference equations" are just and or, if you prefer the " = H_{n+1}- H_n" and " " form then and , for each n.